Conductor temperature rise

NEC Table 8 DC Resistance at 75°C, Note 2: R2 = R1[1+k(T2-75)] where k =0.00323 for copper and T2 = Actual Conductor Temp.

How is T2 arrived at given Actual Ambient Temperature and Actual Operating Current?


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Table 8 of Chapter 9, correct?

The above formula is for determining DC resistances at other than the table's 75°C values. If you wanted to calculate the DC resistance at

100°C, for example.

Neither the table nor the formula say anything about ambient temperatures. This all assumes you have already determined the conductor temp.

Reply to
Paul Hovnanian P.E.

Found what I'm looking for. As I suspected, it's a rearranged version of NM that allows you to derive T2 from Tambient and Operating current.

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R1[1+k(T2-75)] where k

Actual Operating

You figger the resistance in the wire by itself and isolated calculation.. ohms law as you know..this give watts give off of the wire in the form of can look up the watts btu/hr equivalent...which is 3.4 btu's per watt roughly. so if you have 100' of wire producing 1 watt of energy due its resistance... over 100'... then thats .034 btu/ ft/ hr.

If that wire is hung in free air with a breeze the trace levels of heat will be blown away in the wind (warmer air by a billionth of a degree)...if that wire is in a conduit with 50 other wires, no air flow...well that heat would accumulate until the conduit warmed up enough to radiate its heat to the air surrounding...ambient air....which temp varies 50 to 100 degees F in many climates its a variable pal.

One always picks the worst case for his calc though.. I temper that with duty cycle..if its real hot climate but the duty cycle is 10 minutes then I am not going to be as concerned as if the duty cycle is 100% and the climate sometimes peaks 15 degrees warmer than the weather analysis averages.

and if the conduit might be a little long and in the sun... then how hot will the wire get inside that conduit? Well on a roof in the noon sun you can lay a wrench down and 20 minutes later it will be so hot you cant pick it up.

So how hot will that conduit of yours with the slightly undersized but fully loaded conductors get? Toasty.. that will increase the resistance in the wire and make them run even hotter.

Compounding that is the utility grid overload on hot days...the voltage drops...

now... low voltage will not cause your lights to draw more amperage, in fact they will draw less amperage the lower the voltage goes on a 'brown out' kind of day.

But MOTORS..thats a different story... the lower the voltage the less efficient the motor, the more 'slip' you get, the less emf is produced by the motor (reactive current that limits line current)... and the MORE amperage the motor draws.

So now you have outside an over heated conduit, in the hot sun, with wires inside drawing more current than it was designed for... yes its a problem.

But generally not to the wiring with can generally stand some abuse. the motor though over heats..over heating burns out a lot of motors.

So if you are an electrical contractor or engineer and specify accordingly you will be doing a great job... however your construcition costs will be up and competition that goes only by the NEC bare minimums, which do not take into account these contingencies, will beat you on price... the customer is not an EE as a rule so will go the cheaper bid.

thus we have these motor burn out problems.

Accordingly I'd recommend sizing to the NEC minimums in most cases because the loads are diverse and you won't see max current very often anyway...then watch for these long runs of conduit in the hot sun and move these runs to a shaded location for starters. then be sure you have not selected the tiniest wire size you can squeeze by with..if wiring costs are an issue, go to 480 vac motors (HVAC etc) then you can run some real small wire... for instance #12 awg to a 5 ton rated heat pump for instance is approved by Carrier corp and the NEC for its 5 ton 3 phase 480 vac units (with no resistance back up heat)). In that case Id run #10 though because its still cheap, gives some reserve and you can add modest resistance heat later if you want.

480vac though takes you into dangerous ranges especially near the main service with its large feeders.. arc flash and shock hazard are greatest there, especially with 480vac.... 50' away on size 10 wire, arc flash hazard is vastly reduced.

To balance this possible oversized wire scene you fit under rated breakers...for instance you might fit a 25 amp breaker on a 20 amp load, with #8 wire, even though the NEC might allow for a 30 amp breaker on #8 wire...this gives you a safer system due to a faster trip on overloads or a dead short, but the oversize wire to handle the issues discussed above.

When you go to 480 be sure to pull an amply sized ground wire, do not count on the conduit. and make sure you have good bonding the unit cabinet and that the wire itself is pulled all the way back to the distribution panel and bonded to the ground there...that ground should also be verified... I dont recommend the use of 480vac in areas where the unskilled can come in contact with it.

thats why you see a preponderance of 240vac...its safer for those applications.

On retrofits, where 480vac is installed I have seen nothing but the conduit used as a ground. thats not good with

480v... its less of a problem with 240v..

To get back to yer original question: If it looks like its going to get hot oversize the wire to exceed NEC regulations. hair splitting the calc is a waste of time otherwise.

Phil Scott

Phil Scott

Reply to
Phil Scott

R1[1+k(T2-75)] where k

and Actual

other than the

resistance at


the conductor


rearranged version of NM


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Does it mention sun and sun angle on ouside exposed conduit particular long runs often seen on industrial building roof tops?

The solar load can be 5x the ambient air load. Location of the conduit is also crucial, is it on a hot tar and gravel roof? or is its clamped to a cool concrete wall.

These are not minor issues for many motor loads, especially HVAC motors subject to over heating at the worst possible load conditions.

Phil Scott

Reply to
Phil Scott

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